Monomer concentration prediction and control in a polymerization process

ABSTRACT

A method for the control of a polymerization process, which method employs the combination of a densitometer measurement of the polymerization reaction mixture and a quadratic computer model.

BACKGROUND OF THE INVENTION

1. Field of the Invention

This invention relates to a process for the operation of apolymerization reactor for producing polymers. More particularly, thisinvention relates to a method for the control of monomer concentrationin a polymerization process to provide improved control of at least oneof polymer production rate, polymer melt index, and density control.

2. Description of the Prior Art

Although, for sake of clarity and brevity, this invention will bedescribed in respect of the slurry phase polymerization of ethylene toproduce high density polyethylene (HDPE), it is to be understood thatthis invention applies generally to polymerization processes in which aprocess fluid desirably flows in a substantially uniform manner, and inwhich a densitometer is employed. For example, this invention can beapplied in polymerization systems wherein either slurry or solutionpolymerization of at least one monomer takes place.

Heretofore, HDPE has been formed by polymerizing ethylene whiledissolved in a solvent such as isobutane using a silica-supportedchromium/aluminum catalyst. Tri-ethyl borane (TEB) has been employed forvarious reasons, one of which was to form hexene, a co-monomer, in situin the reaction mixture. Ethylene and molecular hydrogen (hydrogen) areadded to form a final reaction mixture. This reaction mixture iscirculated in a continuous stream (loop) in the reactor system, and aslurry is formed which is composed of this mixture and suspended solidpolyethylene particles (powder). A slip stream of this slurry iswithdrawn and solid polyethylene product recovered therefrom. Thereaction is carried out at a temperature of from about 205 to about 225degrees Fahrenheit (F.) and a pressure of from about 600 to about 700psig inside a loop-type reactor that can be, for example, about 24″ ininside diameter, and about 728 feet long. Inside the reactor, thereaction slurry is circulated at a high velocity, e.g., about 35 feetper second, to prevent settling out of the polymer particles in thereactor.

The reaction product is withdrawn from the reactor as a slurry ofpolyethylene powder in liquid isobutane. In order to reduce the amountof isobutane that must be recycled through the purification section, theslurry is concentrated by the use of hydroclones after it leaves thereactor. Hot recycle water is added to the polymer slurry coming out ofthe hydroclones, and the combined streams flow into a high-pressureslurry flash drum where the isobutane and unreacted ethylene are removedoverhead from the top of the drum, and the water and polymer are removedfrom the bottom of the same vessel. A slip stream taken from the overhead gas from the high pressure separator is taken to a conventional gaschromatograph where a sample of the gas is periodically analyzed. Thisperiodic analysis takes from 2 to 3 minutes per analysis cycle andtypically has a 7 to 10 minute delay from real time. The composition ofthis gas sample gives an indication of the actual concentration ofethylene gas inside the slurry loop reactor.

Typically, the ethylene concentration is controlled to about 6 percentby mole (mole %), but, depending on the type of product made, it can bein the range from about 2 to about 8 mole %. The TEB concentration iscontrolled in the range from about 0.4 to about 0.7 ppm. Hydrogen isused to control chain branching. Typically, the hydrogen concentrationin the reactor is in the range from about 0.80 to 1.2 mole %.

Processing conditions in the reactor can be varied to influence thepolymers melt index, molecular weight distribution, and density.Temperature is an important variable in the polymerization process.Depending on the type of polymer resin made, reactor temperature ismaintained at the desired level by circulating tempered water throughjackets carried by the reactor. Around the reactor loop, a number ofconventional thermocouples or resistance temperature detectors (RTD's)are employed for measurement of the temperature of the reaction mixture.Reactor temperature is maintained at the desired level, in part, bycirculating tempered water through the reactor's jackets. The amount ofethylene fed to the reactor directly affects the temperature of thereaction.

In the reactor loop there is a conventional analyzer that measures thedensity of the slurry circulating in the reactor. This instrumentcontinuously measures the density of the slurry which is indicative ofthe polymer solids concentration in the reactor. The solidsconcentration is typically maintained at a desired concentration, e.g.,from about 37 to about 44% by weight (wt. %). This concentration can becontrolled by adjusting the isobutane feed rate to the reactor.

The combined stream of reactor hydroclone bottom flow and hot recyclewater is flashed into a high pressure slurry drum that is maintained ata pressure of from about 220 to about 230 psig. Most of the hydrocarbonsare vaporized by the hot water and are recovered from the overheadstream of the drum by way of a cyclone separator. This cyclone separatesand removes polymer particles from the overhead gas stream. Agitatorshold the solid polymer particles in suspension in the water. The bottomsoutput of the high pressure drum is sent to a low pressure slurry drumwhich is maintained at a pressure below that of the high pressure slurrydrum, e.g., about 1.5 psig. The slurry is thickened in the low pressureslurry drum, and then removed from the agitated section of the drum andpumped to centrifuges. Water from the centrifuges is discharged to therecycle water drum and then pumped to the recycle water separator. Arecycle water separator is used to provide residence time to allowfinely divided polymer powder fines to disengage from the recycle water.Solid polymer particles from the centrifuges are passed into a fluid beddryer. After the fluid bed dryer, the dried polymer is conveyed topowder storage silos or a mixer feed hopper.

The melt index of the polymer in the reactor is controlled mainly by thereaction temperature and ethylene concentration in the reaction mixture.Polymer density is controlled by the concentration of the TEB and/orhexene present in the polymerization reaction mixture.

Process variables in the reactor can change suddenly and their effect onthe ethylene concentration in the reactor may not be picked-up by theaforesaid gas chromatograph since that chromatograph has a 7 to 10minute dead time (feedback delay). This delayed ethylene concentrationanalysis has a good probability from time to time of causing less thandesired reactor production and polymer property control, especiallyduring un-steady state processing conditions. Accordingly, there is aneed for better monomer concentration analysis and control inpolymerization processes such as the HDPE process aforesaid.

Pursuant to this invention, real time, on-line prediction and control ofmonomer concentration inside a polymerization reactor is substantiallyimproved by using certain process instrumentation coupled withmathematical models to provide more consistent reactor control. Pursuantto this invention, a system that employs a densitometer measurement anda mathematical model for monomer concentration prediction reduces theaforesaid time delay by several orders of magnitude, and provides a moreoptimal monomer feed rate control.

SUMMARY OF THE INVENTION

In accordance with this invention, a densitometer measurement and aquadratic mathematical model are coupled into an algorithm whose outputvalue can be used to closely control the monomer concentration in apolymerization reactor under varying steady and unsteady statesituations. This combination provides, in real time, a more optimizedpolymer production rate and improved polymer properties such as densityand melt index.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows a typical slurry loop reactor process flow diagram.

FIG. 2 shows a computer hardware block diagram and logical processinformation flow diagram useful in this invention.

FIG. 3 shows a flow chart of logical software calculation steps usefulin the hardware of FIG. 2.

DETAILED DESCRIPTION OF THE INVENTION

FIG. 1 shows an HDPE slurry polymerization process. A mixture 25 ofethylene, hydrogen, hexene, and isobutane enters horizontal loop reactor15 and joins the reaction mixture slurry that is continuously circulatedwithin reactor 15. The slurry is circulated at a velocity sufficient toprevent settling out of the solid polymer particles inside reactor 15.Catalyst 55 is also fed to the reactor to drive the polymerizationreaction. The heat of polymerization is removed by water that circulatesthrough jackets (not shown) that are mounted on reactor 15.

A conventional, commercially available, on-line densitometer 65 such asa K-RAY Model 3680 that is marketed by Thermo Fisher Scientific, ProcessInstruments Division, Sugar Land, Tex., is used to provide processinformation on the density of the slurry at short time intervals, e.g.,from about every 2 to about every 5 seconds. Densitometer 65 can employgamma beam attenuation for essentially real time read out from ascintillation-based detector. The pulses from the scintillation-detectorare directly related to the intensity of the gamma ray energy received.The pulses are conditioned, counted, and scaled by a built in processorto provide process fluid density read outs with an accuracy up to plusor minus 0.0001 grams per cubic centimeter depending on the fieldcalibration.

A slip stream 85 is removed from reactor 15 and sent to the inlet of acentrifugal separator (hydroclone) 155 where a mixture 135 of solidpolymer particles, isobutane, ethylene and hydrogen is centrifugallyseparated to leave a main isobutane stream 95. The lighter isobutane instream (line) 95 leaves hydroclone 155 and is returned to reactor 15 vialine 75 where it rejoins the circulating reaction slurry in reactor 15.Water 145 is mixed with stream 135 and passed into high pressureseparator 165. A polymer and water mixture 105 is removed from separator165 and separately processed (not shown) as described hereinabove torecover the solid polymer therein as a product of the process. A gaseousmixture 115 of unreacted ethylene, hydrogen and some isobutane isremoved as overhead from separator 165. An on-line gas chromatograph 125is operatively connected to line 115 to measure the mole percent ofethylene and hydrogen at this outlet of separator 165. These are theconcentration measurements that have a lag-time of between 7 to 10minutes.

FIG. 2 shows a block diagram of the computer hardware and logicalprocess information flow pursuant to this invention. Typically, measuredvalues of reaction temperature from at least one RTD, reaction pressurefrom at least one remote sealed pressure transmitter such as a Rosemountmodel 3051, output of ethylene in mole % and hydrogen in mole % asmeasured by the gas chromatograph 125, and slurry density in reactor 15as measured by densitometer 65 are brought into an analog/digitalconverter 21. Converter 21 is in a conventional, commercially available,distributed control system (DCS) 12, such as an Emerson Process System.These process signals are stored in memory, 51, and, throughconventional Emerson interface server 61, are translated and transferredto conventional, commercially available server 13, e.g., a Compaq G3server, and into data acquisition unit 101. From here the data istransferred by time scheduler 71 which periodically causes the operationof the model subroutines 81.

Subroutine unit 81 is where the calculations are performed pursuant tothis invention. Operation of unit 81 is periodically initiated bysubroutine model 130 (FIG. 3). The output of model subroutines unit 81is displayed and stored in memory 91. The calculated ethyleneconcentration value of the model is transferred back into the dataacquisition unit 101, through interface 61, and downloaded into memory51 of DCS 12. From memory 51, the calculated values of the manipulatedvariables such as ethylene flow to the reactor and catalyst flow to thereactor are passed to their respective controllers 41, and a signal sentfrom converter 21 to their respective control valves on reactor 15.These control valves are collectively shown in FIG. 2 at 31. In thisfashion, optimal control of polymer production rate and polymerproperties such as density and melt index is obtained.

FIG. 3 presents a flowchart showing the software calculation steps ofthis invention. The calculation process of this invention starts insoftware model unit 81. Reactor pressure, reactor temperature, ethyleneand hydrogen concentration in mole % as measured by the gaschromatograph 125, and slurry density as measured by densitometer 65.The next step 30 checks for zero values of the foregoing inputparameters, and determines if adequate data is available to perform thecalculations in step 50, or to activate alarm 40 and return to startingpoint 20 to read new values of input parameters or to freeze thecalculation step temporarily until the next calculation cycle.

The first two calculations are performed in step 50. They determine therelative temperature (F.), Equation (1), and relative pressure (Psia),Equation (2), in the slurry reactor according to the followingequations:

TRX=T−200   Equation (1)

PRX=P−585.3   Equation (2)

A composition term (AX) using ethylene (% mole) and hydrogen (% mole) isalso calculated in step 50 according to the following equation:

$\begin{matrix}{{AX} = \frac{\frac{C_{2}^{=}}{2} + \frac{H_{2}}{28.57}}{100}} & {{Equation}\mspace{14mu} (3)}\end{matrix}$

TRX, PRX, and AX are employed in solving various equations set forthhereinafter.

Calculation of liquid density polynomial terms proceeds in step 60according to the following equations (4) through (6), the “*” indicatinga multiplication function:

DENLIQ1=a ₁ +a ₂ TRX+a ₃ AX+a ₄ PRX+a ₅ TRX*AX+a ₆ TRX*PRX*AX+a ₇ TRX ²  Equation (4)

DENLIQ2=DENLIQ1+b ₁ AX ² +b ₂ TRX*AX ² +b ₃ AX ² PRX   Equation (5)

DENLIQ3=DENLIQ2+c ₁ TRX ³   Equation (6)

DENLIQ3 is used in solving Equation (9) below.

The polymer density is calculated in step 70 according to the followingequation:

DENPOL=d₁ +d ₂ TRX   Equation (7)

DENPOL is used in Equations (8) and (9) below.

The liquid density is calculated in step 70 according to the followingequation:

$\begin{matrix}{{DENLIQ} = \frac{\begin{matrix}{{100*{slurrydensity}*{DENPOL}} -} \\{{FSOLIDS}*{slurrydensity}*{DENPOL}}\end{matrix}}{\begin{matrix}{{100*{DENPOL}} -} \\{{FSOLIDS}*{slurrydensity}}\end{matrix}}} & {{Equation}\mspace{14mu} (8)}\end{matrix}$

In Equation (8) FSOLIDS is the filtered solids concentration. The filtersolids concentration is obtained by averaging the QSOLIDS concentrationcalculated from Equation (13) below over a period time around 15minutes.

DENLIQ is used in Equation (13) below.

The solids concentration is calculated in step 80 according to thefollowing equation:

$\begin{matrix}{{QSOLIDS} = \frac{\begin{matrix}{100*{DENPOL}*} \\\left( {{slurrydensity} - {{DELINQ}\; 3}} \right)\end{matrix}}{{Slurrydensity}*\left( {{DENPOL} - {{DELINQ}\; 3}} \right)}} & {{Equation}\mspace{14mu} (9)}\end{matrix}$

The calculation of the constants in the quadratic equation proceeds instep 90 according to the following equations:

QCONSTANTS=e ₁ +e ₂ TRX+e ₃ PRX+e ₄ TRX ² +e ₅ TRX ³   Equation (10)

QA=f ₁ +f ₂ TRX+f ₃ PRX   Equation (11)

QB=g ₁ +g ₂ TRX+g ₃ TRX*PRX   Equation (12)

QC=QCONSTANTS−DENLIQ   Equation (13)

The parameters a_(i),b_(i),c_(i),d_(i),e_(i),f_(i),g_(i) are constantsin each one of the equations shown above and their numerical values areshown in the Table below.

VALUES OF PARAMETERS IN EQUATIONS (4, 5, 6, 7, 10, 11, 12) I ai bi ci diei fi gi 1 0.4633 −0.68998 −0.0000002 0.927 0.4633 −0.68998 −0.36508 2−0.0008884 −0.0300355 0.000307 −0.0008884 −0.030055 −0.0036994 3−0.36508 0.0033084 0.0000462 0.0033084 0.0000239 4 0.0000462 −0.00000825 −0.0036994 −0.0000002 6 0.0000238 7 −0.0000082

Calculation of the real root of a quadratic equation for determinationof the ethylene concentration X (mass), see Equation (15), proceeds instep 100 according to the following equations:

QA*(X ²)+QB*X+QC=0   Equation (14)

The equation above has a real solution that is expressed as:

$\begin{matrix}{X = \frac{{- {QB}} - \sqrt{({QB})^{2} - {4*{QA}*{QC}}}}{2*{QA}}} & {{Equation}\mspace{14mu} (15)}\end{matrix}$

Finally, the concentration of ethylene (mole %) in the slurry loopreactor is calculated in step 110 according to the following equation:

$\begin{matrix}{C_{2}^{=} = {2\left\lbrack {{100*X} - \frac{H_{2}}{28.57}} \right\rbrack}} & {{Equation}\mspace{14mu} (16)}\end{matrix}$

After completion of the foregoing calculations, the calculated resultsare hibernated (temporarily stored) in step 130 until the next cyclewhen the foregoing calculation procedure is repeated.

The aforementioned calculation scheme shown in equations (1) through(16) provides a capability to implement a more consistent (less varied)control of the ethylene concentration in reactor 15 without themagnitude of time lags or delays as were experienced by the prior art byrelying solely on the results of gas chromatograph 125. For example,with the prior art process described hereinabove, the lag time of 7 to10 minutes mentioned hereinabove is reduced to a lag time of from about30 to about 60 seconds.

By controlling the ethylene feed rate to the reactor every 30 to 60seconds, the DCS can then more closely control the reactor temperaturewhich, in turn, provides excellent control of the solids concentrationin the slurry inside the reactor. In addition, the continuous feedbackto the DCS of ethylene concentration on cycles of no more than a minuteenables the DCS to more closely control the density and melt index ofthe polymer product during both steady state reactor behavior andunsteady-state reactor behavior during product transitions. By thisinvention, product transitions can be improved, thereby allowing foroptimization of product properties and plant capacity.

The aforementioned calculation scheme is not limited to horizontal,slurry loop polymerization reactor processes. It can be applied as wellto vertical loop polymerization reactor processes.

1. In a polymerization process for forming in a reaction mixture atleast one polymer from at least one monomer and controlling the physicalproperties of said polymer utilizing at least one process measurementtaken from said polymerization process, said polymerization processemploying a densitometer to obtain the density of said polymerizationreaction mixture containing said at least one monomer, the improvementcomprising: (a) measuring at least one pressure and at least onetemperature in said reaction mixture, calculating the averageconcentration of solids in said reaction mixture, measuring the densityof said reaction mixture with said densitometer, measuring said monomerconcentration, each of said measurements providing an analog signaloutput, and converting said analog signals to digital signals; (b)providing a digital computer with a data base that includes said digitalsignals obtained from step (a); (c) programming said digital computeraccording to a densitometer quadratic concentration model havingconstants and a real root for determining the monomer concentration insaid reaction mixture; (d) calculating at least one physical property ofsaid at least one polymer according to the model of step (c) using thedatabase of step (b); (e) using said at least one calculated physicalproperty of step (d) as a predictor of at least one physical property ofthe polymer produced by said polymerization process, and (f) controllingsaid polymerization process based on said calculated physical property.2. The method of claim 1 where said predicted physical property is atleast one of density and melt index.
 3. The method of claim 1 whereinsaid process is for the slurry polymerization of ethylene in thepresence of hydrogen, and in step (d): (1) a reference temperature iscalculated according to the equationTRX=T−200 (2) a reference pressure is calculated according to theequationPRX=P−585.3 (3) a composition term using ethylene in mole % and hydrogenin mole % is calculated using the equation,${AX} = \frac{\frac{C_{2}^{=}}{2} + \frac{H_{2}}{28.57}}{100}$ (4)liquid density polynomial terms are calculated using the equation,DENLIQ1=a ₁ +a ₂ TRX+a ₃ AX+a ₄ PRX+a ₅ TRX*AX+a ₆TRX*PRX*AX+a₇ TRX ²DENLIQ2=DENLIQ1+b ₁ AX ² +b ₂ TRX*AX ² +b ₃ AX ² PRXDENLIQ3=DENLIQ2+c ₁ TRX ³ (5) a polymer density term is calculated usingthe equation,DENPOL=d ₁ +d ₂ TRX (6) a liquid density term is calculated using theequation, ${DENLIQ} = \frac{\begin{matrix}{{100*{slurrydensity}*{DENPOL}} -} \\{{FSOLIDS}*{slurrydensity}*{DENPOL}}\end{matrix}}{\begin{matrix}{{100*{DENPOL}} -} \\{{FSOLIDS}*{slurrydensity}}\end{matrix}}$ (7) a solids concentration term is calculated using theequation,${QSOLIDS} = \frac{{100*{DENPOL}*\left( {{slurrydensity} - {{DENLIQ}\; 3}} \right)}\;}{{Slurrydensity}*\left( {{DENPOL} - {{DENLIQ}\; 3}} \right)}$(8) said constants in said quadratic concentration model are calculatedare calculated according to the equations,QCONSTANTS=e ₁ +e ₂ TRX+e ₃ PRX+e ₄ TRX ² +e ₅ TRX ³QA=f ₁ +f ₂ TRX+f ₃ PRXQB=g ₁ +g ₂ TRX+g ₃ TRX*PRXQC=QCONSTANTS−DENLIQ (9) said real root in said quadratic concentrationmodel for the determination of the ethylene concentration in saidreaction mixture is calculated using the equations,QA*(X²)+QB*X+QC=0$X = \frac{{- {QB}} - \sqrt{({QB})^{2} - {4*{QA}*{QC}}}}{2*{QA}}$ and(10) the concentration of ethylene monomer in said reaction mixture iscalculated using the equation,$C_{2}^{=} = {2\left\lbrack {{100*X} - \frac{H_{2}}{28.57}} \right\rbrack}$